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Some remarks on the Navier-Stokes equations with a pressure-dependent viscosity. (English) Zbl 0597.35097

This paper studies existence, uniqueness and regularity for solutions to the Navier-Stokes equations, retaining the solenoidal restriction but allowing the viscosity to depend on pressure. Such situations, it is argued, are possible in motions of some organic liquids subjected to pressure variations of several thousand atmospheres.
The pressure dependence of viscosity complicates the problem by allowing the equations to change type. However, it is shown that the Dirichlet boundary-initial value problem is well-posed provided the equations do not change type.
Reviewer: B.Straugham

MSC:

35Q30 Navier-Stokes equations
35R25 Ill-posed problems for PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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References:

[1] DOI: 10.1002/cpa.3160170104 · Zbl 0123.28706 · doi:10.1002/cpa.3160170104
[2] DOI: 10.1063/1.1744583 · doi:10.1063/1.1744583
[3] DOI: 10.1063/1.1744579 · doi:10.1063/1.1744579
[4] Ladyzhenskaya O.A, Academic Press (1968)
[5] DOI: 10.1016/0022-0396(83)90013-X · Zbl 0476.35032 · doi:10.1016/0022-0396(83)90013-X
[6] Smoller J, Springer (1983)
[7] Sobolevskii P.E, AmerMath. Soc. Transl 49 pp 1– (1966)
[8] Stokes G.G., Trans. Cambridge phil.soc. 8 pp 287– (1845)
[9] Temam, R. 1979. ”Navier-Stokes Equations”. North Holland · Zbl 0426.35003
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